LING 360 Lecture Notes - Lecture 37: Natural Number, Lead, Model Theory
2 Dec 2016
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Three conditions that have to be met when we use quantifier prefixes. There will be a question pertaining to this on the exam. The x in px binds to x rather than to x. The one that binds it is the one that has the smallest scope. Free variables are variables that aren"t bound by anything in the expression. Because the same variables can be both bound and free. Here, x in px is free because it is not preceded by any quantifier prefix a is free x in rax is bound by x. In sxy, x is bound by x and y is bound by y. Bound variables, by definition, are variables that are bound by a quantifier prefix. There will be a question about this on the exam. A formula is closed iff it has no occurrences of a free variable. A formula is open iff it has at least one occurrence of a free variable.
